Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

Will climate change increase the risk of plant invasions into mountains?

Mountain ecosystems have been less adversely affected by invasions of non-native plants than most other ecosystems, partially because most invasive plants in the lowlands are limited by climate and cannot grow under harsher high-elevation conditions. However, with ongoing climate change, invasive species may rapidly move upwards and threaten mid- then high-elevation mountain ecosystems. We evaluated this threat by predicting current and future potential distributions of 48 invasive plant species distributed in Switzerland (CH) and New South Wales (NSW), two areas where climate interacts differently with the elevation gradient. Using a species distribution modeling approach combining two scales, which builds on high-resolution data (< 250 m) but accounts for the global climatic niche of species, we found that different environmental drivers limit the elevation range of invasive species in the two regions, leading to region-specific species responses to climate change. Whereas the optimal suitability for plant invaders is predicted to markedly shift from the lowland to the montane or subalpine zone in CH, such an upward shift is far less pronounced in NSW where montane and subalpine elevations are currently already suitable. Non-native species able to invade the upper reaches of mountains in a future climate will be cold-tolerant in the Swiss Alps but preferring wet soils in the Australian Alps. Other plant traits were only marginally associated with elevation limits. These results demonstrate that a more systematic consideration of future distributions of invasive species is required in conservation plans of not yet invaded mountainous ecosystems.